/*

V E K T O R Y N O M I A L S

 rev. 0.031-pari/gp

Released under the terms of use of the: On-Line Encyclopedia Of Integer sequences (R).

(Also available at: http://oeis.org/w/images/a/a7/VEKTORYNOMIALSdot031.txt)

 2013 Feb 19, R. J. Cano.
 
 You might be also interested on this: http://oeis.org/w/images/b/be/Another_Illustration_of_more_symmetries_in_A215940_.txt
  
*/

/* #1 Definition: Abstract Matrix Operator Isomorphically Identical to divide by (Base-1) */
A(n)=-1*matrix(n-1,n-1,i,j,(i<=j));

/* #2 Definition: Concatenation of the first non-negative in ascending order as the smallest possible permutation */
p_smallest(n)=vectorv(n-1,k,k);

/* #3 Definition: Concatenation of the first non-negative in descending order as the greatest possible permutation */
p_greatest(n)=vectorv(n-1,k,n-k-1);

/* #4 Definition: Concatenation of the digits given by the integer serie of the symmetric products: k*(n-k) for k in 1..n-1 */
maximumOfA215940(n)=A(n)*(p_greatest(n)-p_smallest(n));

/* #5 Definition: THE (base-independent-vector) TO (base-dependent-integer) CONVERSION through polynomial interpretation. */
forTheOEIS_maximumOfA215940_in_base_r(n=6,r=if(n<=6,10,1+n^2\4))={my(W=maximumOfA215940(n)); sum(k=1,#W,W[k]*r^(#W-k))};

/*
 * Note(s):
 * 
 * i)   FACT: forTheOEIS_maximumOfA215940_in_base_r(k) is the same than A211869(k). 
 * ii)  FACT: Every term fo the form A215940(q!) for some allowed q should look (the value of the term should look) like a palindrome.
 * iii) FACT: The condition (ii) doesn't affect the terms in A217626 at least for decimal (base "ten").
 * iv)  FACT: The base from where the terms of A215940 properly computed are Universals in the sense of A211869, is given by A033638.
 * v)   FACT: The same treatment based on vectors and matrices is possible with succesful results applied to all the terms of A215940.
 * vi)  CONJECTURE: The triangular array made from the values of the digits present in the maximums for A215940 once they're converted
 * .................in palindromes in the base given by A033638, might be a modification of the Pascal's Trinagle.
 * 
 */

/* Brief showtime */

print("\n");
print("V E K T O R Y N O M I A L S");
print(" ");
print("  rev. 0.031-pari/gp");
print(" ");
print("  Released under the terms of use of the: On-Line Encyclopedia Of Integer sequences (R).");
print("  ");
print("  2013 Feb 19, R. J. Cano.");
print(" ");
print("About A215940, A217626, and A211869. After intensive research and refinement in such matters, it was found that:");
print(" ");

/* Brief showtime */

for(y=1,12,print("A215940(",y,"!) that currently is equals in decimal to ",forTheOEIS_maximumOfA215940_in_base_r(y,10),", actually should be ",forTheOEIS_maximumOfA215940_in_base_r(y)," in order to preserve its palindromic pattern in base ",if(y<=2,3,1+y^2\4)," onwards..."));

print(" ");
print("(End) ");
print("\n");
quit();
/*
 *  << I have already computed a 11! terms b-file without the "offsets" column for A215940. Feel free of Email me requesting a copy. >>
 * 
 *  --R. J. Cano.
 * 
 */